Finite Group Databasebeta

← #10827376

Subgroups — #10827376

Order 768.

1500 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5695C211yesmaximal, characteristic, complemented
2C2×#4773C211yesmaximal, characteristic, complemented
3C2×D3×#102C211yesmaximal, characteristic, complemented
4#76436C211yesmaximal, characteristic, complemented
5C3×#2025C211yesmaximal, characteristic, complemented
6#71743C211yesmaximal, characteristic, complemented
7#70204C211yesmaximal, characteristic, complemented
8#70201C211yesmaximal, characteristic, complemented
9#69657C211yesmaximal, characteristic, complemented
10#68886C211yesmaximal, characteristic, complemented
11#68883C211yesmaximal, characteristic, complemented
12#68881C211yesmaximal, characteristic, complemented
13#68872C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68668C211yesmaximal, characteristic, complemented
16#23963—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic, complemented
19C2×#938C2211yescharacteristic
20C22×#213C2211yescharacteristic
21C22×D24C2211yescharacteristic
22C22×D3×C8C2211yescharacteristic
23#5695—24no—
24#5695—24no—
25C2×#898—21no—
26C2×#895—21no—
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#895C2211yescharacteristic, complemented
30C2×#894—21no—
31C2×#893—21no—
32C2×#892C2211yescharacteristic, complemented
33C2×D3×C4⋊C4C2211yescharacteristic
34C2×#882—21no—
35C2×C4×D12C2211yescharacteristic
36C2×C4×D12C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic, complemented
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
46#4987C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic, complemented
50#4961—21no—
51#4960—21no—
52#4955—21no—
53#4939C2211yescharacteristic
54#4773—24no—
55D3×#102—24no—
56C3×#340C2211yescharacteristic, complemented
57C3×#340C2211yescharacteristic, complemented
58C3×#336C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4524C2211yescharacteristic, complemented
64C2×#553—31no—
65C2×#447—31no—
66C22×#102—31no—
67#2408—31no—
68#2025—31no—
69#2025D311yescharacteristic, complemented
70#1999—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1879—31no—
75#1875—31no—
76#1875—31no—
77#1869—31no—
78#1824—31no—
79C24×D3—21no—
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C2×D3×D4—22no—
84C2×D3×D4—22no—
85C2×D3×D4—22no—
86C2×D3×D4—22no—
87C2×D3×D4—41no—
88C2×D3×D4—41no—
89C22×D12—21no—
90C22×D12—21no—
91C22×D12—21no—
92C22×D12D411yescharacteristic
93C22×D12C2311yescharacteristic
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C22×C4×D3C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C3×#125—22no—
102C3×#125—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C42C2311yescharacteristic
111C2×#217—21no—
112#938—22no—
113#938—41no—
114C2×#213—22no—
115C2×#213—22no—
116C2×#213—41no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—21no—
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C2×D24—22no—
135C2×D24—22no—
136C2×D24—41no—
137C2×D3×C8—22no—
138C2×D3×C8—41no—
139C2×D3×C8—41no—
140#898—28no—
141#895—28no—
142#895—22no—
143#895—22no—
144#895—22no—
145#895—22no—
146#895—41no—
147#895D414yescomplemented
148#894—28no—
149#893—28no—
150#892—22no—
151#892—22no—
152D3×C4⋊C4—22no—
153D3×C4⋊C4D414yescomplemented
154#882—44no—
155C4×D12—22no—
156C4×D12—22no—
157C4×D12—22no—
158C4×D12—22no—
159C3×#102—22no—
160C3×#102—22no—
161#832—22no—
162C3⋊#95—21no—
163#821—22no—
164#821—41no—
165(C2×D3)⋊C8—22no—
166(C2×D3)⋊C8—41no—
167(C2×D3)⋊C8—41no—
168#809—22no—
169#809—22no—
170#809—41no—
171C23×D4—31no—
172C22×D8—31no—
173C22×D8—31no—
174C23×C8—31no—
175#553—64no—
176#553—64no—
177C2×#126—61no—
178C2×#125C2×D311yescharacteristic, complemented
179C2×#123—61no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—31no—
184C2×#121—61no—
185C2×#120—61no—
186C2×C4×D4—31no—
187C2×C4×D4—31no—
188C2×C4×D4—61no—
189C2×#117—31no—
190C22×C4⋊C4—31no—
191#447—64no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—64no—
199C2×#102C2×D311yescharacteristic
200C2×#102C2×D311yescharacteristic
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8—31no—
204#394—61no—
205#392—61no—
206#390—31no—
207#390C2×D311yescharacteristic
208#380—31no—
209#379—61no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic, complemented
215#340C2×D311yescharacteristic, complemented
216#336—31no—
217#336C2×D311yescharacteristic, complemented
218C24×C3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—42no—
222C23×D3—42no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—81no—
227C23×D3—81no—
228C23×D3C2×D411yescharacteristic
229C23×D3C2×D411yescharacteristic
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4#4112yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—81no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252D3×D4—28no—
253D3×D4—44no—
254D3×D4—44no—
255D3×D4—44no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—22no—
265C2×D12—24no—
266C2×D12—22no—
267C2×D12—22no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—24no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12—42no—
274C2×D12—42no—
275C2×D12—81no—
276C2×D12—81no—
277C2×D12—81no—
278C2×D12C2×D412yes—
279C2×D12#4112yes—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—81no—
293C2×C4×D3—81no—
294C2×C4×D3—81no—
295C2×C4×D3—81no—
296C2×C4×D3C2×D412yes—
297C2×C4×D3C2×D412yes—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C3×C4⋊C4—24no—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4C2×D412yes—
311C3×C4⋊C4C2×D412yes—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—81no—
314C3×C42—21no—
315C3×C42—21no—
316#217—42no—
317#213—44no—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—22no—
322(C2×D3)⋊C4—22no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—81no—
328C4⋊Dic3—21no—
329C4⋊Dic3—22no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3C2×D412yes—
333Dic3⋊C4—24no—
334C4×Dic3—24no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341D24—44no—
342D3×C8—44no—
343C25—61no—
344C22×D4—31no—
345C22×D4—31no—
346C22×D4—31no—
347C22×D4—61no—
348C22×D4—61no—
349C22×D4—61no—
350C22×D4—62no—
351C22×D4—62no—
352C22×D4—61no—
353C22×D4—62no—
354C22×D4—62no—
355C22×D4—61no—
356C22×D4—121no—
357C22×D4—121no—
358C22×D4C22×D311yescharacteristic
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—61no—
362C23×C4—61no—
363C2×D8—62no—
364C2×D8—62no—
365C2×D8—62no—
366C2×D8—62no—
367C2×D8—121no—
368C2×D8—121no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—62no—
372C22×C8—121no—
373C22×C8—121no—
374C22×C8C22×D311yescharacteristic
375C22×C8C22×D311yescharacteristic
376#126—68no—
377#125—22no—
378#125—22no—
379#123—68no—
380#121—34no—
381#121—62no—
382#121—62no—
383#121—68no—
384#121—62no—
385#121—62no—
386#121—62no—
387#121—121no—
388#121—121no—
389#120—124no—
390C4×D4—62no—
391C4×D4—62no—
392C4×D4—62no—
393C4×D4—62no—
394C4×D4—68no—
395#117—62no—
396#117—62no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—61no—
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—31no—
411C2×C22⋊C4—31no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C42—61no—
422C2×C42C22×D311yescharacteristic
423#102—22no—
424#102—22no—
425#102—62no—
426#102—62no—
427#102—62no—
428#102—62no—
429#102—121no—
430#102—121no—
431C22⋊C8—62no—
432C22⋊C8—121no—
433C22⋊C8—121no—
434#95—61no—
435C23×C3—22no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3C22×D411yescharacteristic
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—48no—
457C22×D3—41no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—84no—
470C22×D3—84no—
471C22×D3—84no—
472C22×D3—84no—
473C22×D3—84no—
474C22×D3—84no—
475C22×D3#12012yes—
476C22×D3#13512yes—
477C22×D3AGL(1,ℤ/8)12yes—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—41no—
481C3×D4—41no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C22×D411yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500C2×C3×C4C2×#4111yescharacteristic
501C2×C3×C4H(5,𝔽2)11yescharacteristic
502C2×C3×C4H(5,𝔽2)11yescharacteristic
503#67—48no—
504#67—84no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3#12012yes—
517D12—22no—
518D12—22no—
519D12—22no—
520D12—22no—
521D12—44no—
522D12—48no—
523D12—41no—
524D12—41no—
525D12—41no—
526D12—41no—
527D12—84no—
528D12—84no—
529C4×D3—22no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—41no—
534C4×D3—41no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3—84no—
538C4×D3—84no—
539C3×C8—41no—
540C3×C8—41no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C24—21no—
544C24—31no—
545C24—31no—
546C24—61no—
547C24—61no—
548C24—122no—
549C24—122no—
550C24—122no—
551C24—122no—
552C24—122no—
553C24—241no—
554C24—241no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—32no—
561C2×D4—32no—
562C2×D4—64no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4—62no—
566C2×D4—64no—
567C2×D4—68no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—61no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—122no—
579C2×D4—122no—
580C2×D4—122no—
581C2×D4—122no—
582C2×D4—122no—
583C2×D4—124no—
584C2×D4—124no—
585C2×D4—124no—
586C2×D4—122no—
587C2×D4—122no—
588C2×D4—122no—
589C2×D4—122no—
590C2×D4—241no—
591C2×D4—241no—
592C2×D4—241no—
593C2×D4—241no—
594C2×D4#23912yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—31no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—31no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—241no—
617C22×C4—241no—
618C22×C4—241no—
619C22×C4—241no—
620C22×C4D3×D411yescharacteristic
621C22×C4D3×D411yescharacteristic
622C22×C4C23×D311yescharacteristic
623D8—124no—
624D8—124no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—61no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—124no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—32no—
645C4⋊C4—64no—
646C4⋊C4—62no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4D3×D412yes—
651C4⋊C4D3×D412yes—
652C22⋊C4—42no—
653C22⋊C4—62no—
654C22⋊C4—64no—
655C22⋊C4—62no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—81no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C22⋊C4—122no—
664C22⋊C4—241no—
665C42—21no—
666C42—21no—
667C42—64no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3C2×#12011yescharacteristic
676C22×C3#54611yescharacteristic
677C22×C3#54611yescharacteristic
678C22×C3C2×#13511yescharacteristic
679C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
680C22×C3#57611yescharacteristic
681C22×C3#57611yescharacteristic
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—41no—
689C2×D3—42no—
690C2×D3—42no—
691C2×D3—41no—
692C2×D3—42no—
693C2×D3—42no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—42no—
698C2×D3—41no—
699C2×D3—42no—
700C2×D3—41no—
701C2×D3—816no—
702C2×D3—81no—
703C2×D3—81no—
704C2×D3—81no—
705C2×D3—81no—
706C2×D3—81no—
707C2×D3—81no—
708C2×D3—81no—
709C2×D3—81no—
710C2×D3#44914yes—
711C3×C4—41no—
712C3×C4—42no—
713C3×C4—41no—
714C3×C4—42no—
715C3×C4—81no—
716C3×C4#52511yescharacteristic
717C3×C4#53511yescharacteristic
718C3×C4#54611yescharacteristic
719C3×C4#54611yescharacteristic
720Dic3—22no—
721Dic3—41no—
722Dic3—42no—
723Dic3—81no—
724C23—22no—
725C23—32no—
726C23—32no—
727C23—32no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—61no—
738C23—62no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—62no—
745C23—61no—
746C23—61no—
747C23—128no—
748C23—121no—
749C23—121no—
750C23—121no—
751C23—121no—
752C23—121no—
753C23—121no—
754C23—121no—
755C23—121no—
756C23—121no—
757C23—121no—
758C23—121no—
759C23—121no—
760C23—244no—
761C23—244no—
762C23—244no—
763C23—244no—
764C23—244no—
765C23—244no—
766C23C2×D3×D411yescharacteristic
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—62no—
772D4—62no—
773D4—62no—
774D4—62no—
775D4—124no—
776D4—128no—
777D4—128no—
778D4—121no—
779D4—121no—
780D4—121no—
781D4—121no—
782D4—244no—
783D4—244no—
784D4—244no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—32no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—121no—
812C2×C4—121no—
813C2×C4—121no—
814C2×C4—121no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—244no—
821C2×C4—244no—
822C2×C4C2×D3×D411yescharacteristic
823C2×C4C2×D3×D411yescharacteristic
824C2×C4C2×#23911yescharacteristic
825C2×C4D3×#4111yescharacteristic
826C2×C4#100911yescharacteristic
827C2×C4#100911yescharacteristic
828C8—41no—
829C8—41no—
830C8—121no—
831C8—121no—
832C2×C3—82no—
833C2×C3#240411yescharacteristic
834C2×C3C2×#44911yescharacteristic
835C2×C3#300811yescharacteristic
836C2×C3#329711yescharacteristic
837C2×C3#329711yescharacteristic
838C2×C3#331811yescharacteristic
839C2×C3#331811yescharacteristic
840D3—24no—
841D3—81no—
842D3—82no—
843D3—82no—
844C22—34no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—122no—
862C22—122no—
863C22—121no—
864C22—122no—
865C22—121no—
866C22—122no—
867C22—122no—
868C22—121no—
869C22—121no—
870C22—122no—
871C22—2416no—
872C22—241no—
873C22—241no—
874C22—241no—
875C22—241no—
876C22—241no—
877C22—241no—
878C22—241no—
879C22—241no—
880C22D3×#12011yescharacteristic
881C22#563011yescharacteristic
882C22#567611yescharacteristic
883C22D3×#13511yescharacteristic
884C22#576911yescharacteristic
885C22D3×AGL(1,ℤ/8)11yescharacteristic
886C22#577411yescharacteristic
887C4—41no—
888C4—42no—
889C4—41no—
890C4—42no—
891C4—62no—
892C4—81no—
893C4—121no—
894C4—122no—
895C4—241no—
896C4#562711yescharacteristic
897C4#563011yescharacteristic
898C4#567411yescharacteristic
899C4#567611yescharacteristic
900C3#2396311yescharacteristic, complemented, Sylow
901C2—64no—
902C2—82no—
903C2—241no—
904C2—242no—
905C2—242no—
906C2#7686311yescharacteristic
907C2D3×#44911yescharacteristic
908C2#8008511yescharacteristic
909C2#8118711yescharacteristic
910C2#8119111yescharacteristic
911C2#8165311yescharacteristic
912C2#8172711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2025C2
socleC23×C3C22×D4
hypercenter#2025D3
hypocenterC3#23963
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#5695C2semidirect
2. C2×#4773C2semidirect
3. C2×D3×#102C2semidirect
4. #76436C2semidirect
5. C3×#2025C2semidirect
6. #71743C2semidirect
7. #70204C2semidirect
8. #70201C2semidirect
9. #69657C2semidirect
10. #68886C2semidirect
11. #68883C2semidirect
12. #68881C2semidirect
13. #68872C2semidirect
14. #68673C2semidirect
15. #68668C2semidirect
18. C2×C3×#125C22semidirect
29. C2×#895C22semidirect
32. C2×#892C22semidirect
36. C2×C4×D12C22semidirect
42. C2×#821C22semidirect
44. C2×(C2×D3)⋊C8C22semidirect
45. C2×(C2×D3)⋊C8C22semidirect
49. C2×#809C22semidirect
56. C3×#340C22semidirect
57. C3×#340C22semidirect
58. C3×#336C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4524C22semidirect
69. #2025D3semidirect
147. #895D4semidirect
153. D3×C4⋊C4D4semidirect
178. C2×#125C2×D3semidirect
214. #340C2×D3semidirect
215. #340C2×D3semidirect
217. #336C2×D3semidirect
900. C3#23963semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#56952
C2×#47732
C2×D3×#1022
#764362
C3×#20252
#717432
#702042
#702012
#696572
#688862
#688832
#688812
#688722
#686732
#686682
#239633